A vector network analyzer (VNA) measures a performance of a radio frequency (RF) and/or microwave/millimeter wave device under test (DUT) and produces measured results in terms of network scattering parameters. Network scattering parameters, more commonly known as ‘S-parameters’, are transmission and reflection (T/R) coefficients for the DUT computed from measurements of voltage waves traveling toward and away from a port or ports of the DUT. In general, an S-parameter is expressed either in terms of a magnitude and phase or in an equivalent form as a complex number, the complex number having a real part and an imaginary part. A set of four such S-parameters, namely S11, S12, S21, and S22 each represented by a complex number, provide a complete characterization of linear RF performance of a given two-port DUT at a single frequency. Similarly, a series or sequence of S-parameters, each member of the sequence having been measured at one of multiple different frequencies across an operational frequency range of the DUT, characterizes a frequency performance of the DUT.
As with all test and measurement equipment, VNAs introduce errors into measured S-parameter data produced for a given DUT. The presence of these errors distorts or corrupts the measurements of actual S-parameter data for the DUT. Fortunately, the effects of at least the so-called ‘systematic’ errors introduced by the VNA and any associated test system (e.g., cables, connectors, fixture, etc) may be characterized and subsequently removed from measurements of the DUT. Such a characterization and subsequent removal of the systematic error effects are generally known as VNA calibration.
In simple terms, a VNA calibration involves measuring S-parameters of a set of specialized devices known as ‘calibration standards’ using the VNA being calibrated. A set of error coefficients for an error model of the VNA is then computed from the measured S-parameters using known values of certain defining parameters of the calibration standards. Once computed, the error coefficients may be used to apply a correction to ‘raw’ or ‘as measured’ S-parameter data produced by the VNA for the DUT. The correction so applied mathematically to the data essentially removes the effects of the systematic errors from the raw S-parameter data yielding ‘error corrected’ or ‘calibrated’ measured S-parameter data for the DUT. Thus, the calibrated or error corrected data for the DUT generally represents, or is interpreted as being, an accurate indication of an ‘actual’ performance for the DUT independent of the VNA.
Unfortunately, it is not always convenient or even possible, in many cases, to construct and/or characterize a set of calibration standards, the defining parameters of which are known with sufficient accuracy for calibration purposes over a frequency range of interest. An example of such a situation where constructing and/or characterizing calibration standards is difficult occurs when testing a DUT that must be mounted in a test fixture. Another related example is where the DUT is embedded in a printed circuit board (PCB). Moreover, even in cases where it is possible to manufacture precision standards, the calibration standards may be very expensive owing to a need to control and accurately characterize the performance of such standards. The high cost of precision calibration standards may effectively prohibit their use in many cost sensitive enterprises.
Accordingly, it would be advantageous to calibrate a VNA without relying on using a set of calibration standards having accurately known characteristics. Such a calibration would solve a long-standing need in the area of calibrating a VNA using calibration standards.